The Sample Standard Deviations and Sample Sizes Are Given for Independent

question 53

Multiple Choice

The sample standard deviations and sample sizes are given for independent simple random samples from twopopulations. Use the two-standard-deviations F-test to conduct the required hypothesis test.
- $\mathrm { s } _ { 1 } = 20.9 , \mathrm { n } _ { 1 } = 16 , \mathrm {~s} _ { 2 } = 22.2 , \mathrm { n } _ { 2 } = 13$ ; two-tailed test, $\alpha = 0.05$

• A)Test statistic: \(\mathrm { F } = 0.89\). Critical values \(= 0.338,3.18\). Do not reject \(\mathrm { H } _ { 0 }\).
• B) Test statistic: \(\mathrm { F } = 0.89\). Critical values \(= 0.403,2.62\). Reject \(\mathrm { H } _ { 0 }\).
• C) Test statistic: \(\mathrm { F } = 0.89\). Critical values \(= 0.338,3.18\). Reject \(\mathrm { H } _ { 0 }\).
• D) Test statistic: \(\mathrm { F } = 0.89\). Critical values \(= 0.314,3.18\). Do not reject \(\mathrm { H } _ { 0 }\).

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Definitions:

Win%

A statistical representation, often in sports, denoting the percentage of games or matches won by a team or individual.

Residuals

Differences between observed values and the expected values predicted by a model, used as a diagnostic measure to assess the fit of a statistical model.

Least Squares

A method used in regression analysis to determine the best fit line by minimizing the sum of the squares of the differences between observed and predicted values.

Goals/G

A statistical measurement often used in sports to quantify the average number of goals scored per game by a team or player.